Percent Error Calculator (with Formula)
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Percent Error Calculator
Percent error tells you how close a measured or experimental value is to the accepted true value, as a percentage. It is the standard way to report accuracy in chemistry, physics, and engineering labs. This page also finds the percent uncertainty of a measurement from its ± range.
The percent error formula
Percent error = |Experimental − Theoretical| ÷ |Theoretical| × 100
Example: an experiment measures the density of water as 0.98 g/mL when the true value is 1.00 g/mL. The percent error is |0.98 − 1.00| ÷ 1.00 × 100 = 2%. The absolute error is 0.02; dividing by the true value turns it into a percentage you can compare across experiments.
Percent uncertainty
A measurement is often written as a value plus or minus an uncertainty, like 50 cm ± 0.5 cm. The percent uncertainty is the uncertainty as a percentage of the value: 0.5 ÷ 50 × 100 = 1%. Smaller percent uncertainty means a more precise measurement.
Percent error vs. percentage difference
Use percent error when one value is a known, accepted true value. When neither number is the reference — comparing two independent measurements, for instance — use the percentage difference calculator, which divides by their average instead.
FAQs
Percent error = |experimental − theoretical| ÷ |theoretical| × 100. It measures how far a measured value falls from the accepted true value, as a percentage.
Subtract the true value from your measured value, take the absolute value, divide by the true value, and multiply by 100. If you measured 9.8 but the true value is 10: |9.8 − 10| ÷ 10 × 100 = 2% error.
By the standard formula, no — the absolute value makes it non-negative. Some courses drop the absolute value to show whether the measurement was too high or too low; this calculator reports the standard non-negative percent error.
Percent uncertainty expresses a measurement's uncertainty as a percentage of the value: |uncertainty| ÷ |value| × 100. A reading of 50 cm ± 0.5 cm has a percent uncertainty of 0.5 ÷ 50 × 100 = 1%.
Percent error compares a measurement to a known true value. Percentage difference compares two values of equal standing with no 'correct' one, dividing by their average instead. Use percent error in the lab against an accepted value.